blockoperator.hpp

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// Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.

#ifndef MFEM_BLOCKOPERATOR
#define MFEM_BLOCKOPERATOR

#include "../config/config.hpp"
#include "../general/array.hpp"
#include "operator.hpp"
#include "blockvector.hpp"

namespace mfem
{

//! @class BlockOperator
/**
 * \brief A class to handle Block systems in a matrix-free implementation.
 *
 * Usage:
 * - Use one of the constructors to define the block structure.
 * - Use SetDiagonalBlock or SetBlock to fill the BlockOperator
 * - Use the method Mult and MultTranspose to apply the operator to a vector.
 *
 * If a block is not set, it is assumed to be a zero block.
 */
class BlockOperator : public Operator
{
public:
   //! Constructor for BlockOperators with the same block-structure for rows and
   //! columns.
   /**
    *  offsets: offsets that mark the start of each row/column block (size
    *  nRowBlocks+1).  Note: BlockOperator will not own/copy the data contained
    *  in offsets.
    */
   BlockOperator(const Array<int> & offsets);
   //! Constructor for general BlockOperators.
   /**
    *  row_offsets: offsets that mark the start of each row block (size
    *  nRowBlocks+1).  col_offsets: offsets that mark the start of each column
    *  block (size nColBlocks+1).  Note: BlockOperator will not own/copy the
    *  data contained in offsets.
    */
   BlockOperator(const Array<int> & row_offsets, const Array<int> & col_offsets);

   //! Add block op in the block-entry (iblock, iblock).
   /**
    * iblock: The block will be inserted in location (iblock, iblock).
    * op: the Operator to be inserted.
    * c: optional scalar multiple for this block.
    */
   void SetDiagonalBlock(int iblock, Operator *op, double c = 1.0);
   //! Add a block op in the block-entry (iblock, jblock).
   /**
    * irow, icol: The block will be inserted in location (irow, icol).
    * op: the Operator to be inserted.
    * c: optional scalar multiple for this block.
    */
   void SetBlock(int iRow, int iCol, Operator *op, double c = 1.0);

   //! Return the number of row blocks
   int NumRowBlocks() const { return nRowBlocks; }
   //! Return the number of column blocks
   int NumColBlocks() const { return nColBlocks; }

   //! Check if block (i,j) is a zero block
   int IsZeroBlock(int i, int j) const { return (op(i,j)==NULL) ? 1 : 0; }
   //! Return a reference to block i,j
   Operator & GetBlock(int i, int j)
   { MFEM_VERIFY(op(i,j), ""); return *op(i,j); }
   //! Return a reference to block i,j (const version)
   const Operator & GetBlock(int i, int j) const
   { MFEM_VERIFY(op(i,j), ""); return *op(i,j); }
   //! Return the coefficient for block i,j
   double GetBlockCoef(int i, int j) const
   { MFEM_VERIFY(op(i,j), ""); return coef(i,j); }
   //! Set the coefficient for block i,j
   void SetBlockCoef(int i, int j, double c)
   { MFEM_VERIFY(op(i,j), ""); coef(i,j) = c; }

   //! Return the row offsets for block starts
   Array<int> & RowOffsets() { return row_offsets; }
   //! Read only access to the row offsets for block starts
   const Array<int> & RowOffsets() const { return row_offsets; }
   //! Return the columns offsets for block starts
   Array<int> & ColOffsets() { return col_offsets; }
   //! Read only access to the columns offsets for block starts
   const Array<int> & ColOffsets() const { return col_offsets; }

   /// Operator application
   virtual void Mult (const Vector & x, Vector & y) const;

   /// Action of the transpose operator
   virtual void MultTranspose (const Vector & x, Vector & y) const;

   ~BlockOperator();

   //! Controls the ownership of the blocks: if nonzero, BlockOperator will
   //! delete all blocks that are set (non-NULL); the default value is zero.
   int owns_blocks;

private:
   //! Number of block rows
   int nRowBlocks;
   //! Number of block columns
   int nColBlocks;
   //! Row offsets for the starting position of each block
   Array<int> row_offsets;
   //! Column offsets for the starting position of each block
   Array<int> col_offsets;
   //! 2D array that stores each block of the operator.
   Array2D<Operator *> op;
   //! 2D array that stores a coefficient for each block of the operator.
   Array2D<double> coef;

   //! Temporary Vectors used to efficiently apply the Mult and MultTranspose methods.
   mutable BlockVector xblock;
   mutable BlockVector yblock;
   mutable Vector tmp;
};

//! @class BlockDiagonalPreconditioner
/**
 * \brief A class to handle Block diagonal preconditioners in a matrix-free implementation.
 *
 * Usage:
 * - Use the constructors to define the block structure
 * - Use SetDiagonalBlock to fill the BlockOperator
 * - Use the method Mult and MultTranspose to apply the operator to a vector.
 *
 * If a block is not set, it is assumed to be an identity block.
 *
 */
class BlockDiagonalPreconditioner : public Solver
{
public:
   //! Constructor that specifies the block structure
   BlockDiagonalPreconditioner(const Array<int> & offsets);
   //! Add a square block op in the block-entry (iblock, iblock).
   /**
    * iblock: The block will be inserted in location (iblock, iblock).
    * op: the Operator to be inserted.
    */
   void SetDiagonalBlock(int iblock, Operator *op);
   //! This method is present since required by the abstract base class Solver
   virtual void SetOperator(const Operator &op) { }

   //! Return the number of blocks
   int NumBlocks() const { return nBlocks; }

   //! Return a reference to block i,i.
   Operator & GetDiagonalBlock(int iblock)
   { MFEM_VERIFY(op[iblock], ""); return *op[iblock]; }

   //! Return a reference to block i,i (const version).
   const Operator & GetDiagonalBlock(int iblock) const
   { MFEM_VERIFY(op[iblock], ""); return *op[iblock]; }

   //! Return the offsets for block starts
   Array<int> & Offsets() { return offsets; }

   //! Read only access to the offsets for block starts
   const Array<int> & Offsets() const { return offsets; }

   /// Operator application
   virtual void Mult (const Vector & x, Vector & y) const;

   /// Action of the transpose operator
   virtual void MultTranspose (const Vector & x, Vector & y) const;

   ~BlockDiagonalPreconditioner();

   //! Controls the ownership of the blocks: if nonzero,
   //! BlockDiagonalPreconditioner will delete all blocks that are set
   //! (non-NULL); the default value is zero.
   int owns_blocks;

private:
   //! Number of Blocks
   int nBlocks;
   //! Offsets for the starting position of each block
   Array<int> offsets;
   //! 1D array that stores each block of the operator.
   Array<Operator *> op;
   //! Temporary Vectors used to efficiently apply the Mult and MultTranspose
   //! methods.
   mutable BlockVector xblock;
   mutable BlockVector yblock;
};

//! @class BlockLowerTriangularPreconditioner
/**
 * \brief A class to handle Block lower triangular preconditioners in a
 * matrix-free implementation.
 *
 * Usage:
 * - Use the constructors to define the block structure
 * - Use SetBlock() to fill the BlockOperator
 * - Diagonal blocks of the preconditioner should approximate the inverses of
 *   the diagonal block of the matrix
 * - Off-diagonal blocks of the preconditioner should match/approximate those of
 *   the original matrix
 * - Use the method Mult() and MultTranspose() to apply the operator to a vector.
 *
 * If a diagonal block is not set, it is assumed to be an identity block, if an
 * off-diagonal block is not set, it is assumed to be a zero block.
 *
 */
class BlockLowerTriangularPreconditioner : public Solver
{
public:
   //! Constructor for BlockLowerTriangularPreconditioners with the same
   //! block-structure for rows and columns.
   /**
    *  @param offsets  Offsets that mark the start of each row/column block
    *                  (size nBlocks+1).
    *
    *  @note BlockLowerTriangularPreconditioner will not own/copy the data
    *  contained in @a offsets.
    */
   BlockLowerTriangularPreconditioner(const Array<int> & offsets);

   //! Add block op in the block-entry (iblock, iblock).
   /**
    * @param iblock  The block will be inserted in location (iblock, iblock).
    * @param op      The Operator to be inserted.
    */
   void SetDiagonalBlock(int iblock, Operator *op);
   //! Add a block op in the block-entry (iblock, jblock).
   /**
    * @param iRow, iCol  The block will be inserted in location (iRow, iCol).
    * @param op          The Operator to be inserted.
    */
   void SetBlock(int iRow, int iCol, Operator *op);
   //! This method is present since required by the abstract base class Solver
   virtual void SetOperator(const Operator &op) { }

   //! Return the number of blocks
   int NumBlocks() const { return nBlocks; }

   //! Return a reference to block i,j.
   Operator & GetBlock(int iblock, int jblock)
   { MFEM_VERIFY(op(iblock,jblock), ""); return *op(iblock,jblock); }

   //! Return the offsets for block starts
   Array<int> & Offsets() { return offsets; }

   /// Operator application
   virtual void Mult (const Vector & x, Vector & y) const;

   /// Action of the transpose operator
   virtual void MultTranspose (const Vector & x, Vector & y) const;

   ~BlockLowerTriangularPreconditioner();

   //! Controls the ownership of the blocks: if nonzero,
   //! BlockLowerTriangularPreconditioner will delete all blocks that are set
   //! (non-NULL); the default value is zero.
   int owns_blocks;

private:
   //! Number of block rows/columns
   int nBlocks;
   //! Offsets for the starting position of each block
   Array<int> offsets;
   //! 2D array that stores each block of the operator.
   Array2D<Operator *> op;

   //! Temporary Vectors used to efficiently apply the Mult and MultTranspose
   //! methods.
   mutable BlockVector xblock;
   mutable BlockVector yblock;
   mutable Vector tmp;
   mutable Vector tmp2;
};

}

#endif /* MFEM_BLOCKOPERATOR */